I was thinking of making this a game for geo's (but if you want more i will)


The Missing Square


This is a problem that has perplexed people for years. In the second triangle, where does the extra square come from?.

http://www.niabco.net/dl/puzzle1.gif

i will be interested in some of the answers
post here

200 Geo`s to the first player to get the correct answer.. :cheesy

Light blue..... 1.5 mins to find.......

the hypotenuses aren't the same

the hypotenuses aren't the same

yeah they are..... Is there supposed to be a trick that I walked into......

As games master has kindly offered to cough up... MOVED TO GAMES FOR GEOS :)

T.

No its not solvable.This is an old magicians trick from 50+ years ago. I remeber this in highschool.

Dude, it is a light blue square, the lightest blue. The blue one on the top in picture 2, the one on the left on picture 1

13 * 5 / 2 = 32.5 square units. That's the apparent size of both
combined (whole) triangles. But if you calculate the areas of each of
the sections, again as they appear on the puzzle, they add up to 32
square units on the top one, and 33 square units on the bottom (the
one with the white square in it). This is because the hypotenuses
of both triangles are not straight lines; both are arcs, with a net
area of one square unit.

Light blue square

Pretty sure you cant solve or explain this mathematically.

The 2 non-triangle things simply do not fit. Just like in Tetris, the lengths of the gap and bay do not fit.

I will put a detailed answer here in a few hours (need to make some pictures first), stay tuned! ;icoffee

1 light blue square is missing.........


Am I invisible?

1 light blue square is missing.........
Erm, no?
The parts are all the same!? Just compared them.
The triangles are the same. 8x3 blocks, hypotenuse is 4,7 mm on my screen resolution.

Sheesh..do I need to explain my explanation..lol.

If you look at the two blue triangles which have changed position. Their hypotenuse (the long edge of each triangle) is a different angle. If you look very closely at the top image you can see this..it's very slight, but the line is not straight, it's slightly concave, i.e. it dips in the middle. When you switch the two triangles around you reverse the effect and the hypotenuse of the bottom image is slightly convex...i.e. it bulges out. The difference in area this makes up is equal to one whole square and that is where the extra cube comes from.

If anything it's an optical illusion....you think the two images are triangles and therefore usual rules of geometry would seem to make this problem impossible to solve....apply basic rules of geometry to the individual triangles within the big triangle and the answer is straightforward.

ohCurry's paradox

Othafa's right. I remember this one from years ago. They're different triangles, so they have different area.

the hypotenuses aren't the same


13 * 5 / 2 = 32.5 square units. That's the apparent size of both
combined (whole) triangles. But if you calculate the areas of each of
the sections, again as they appear on the puzzle, they add up to 32
square units on the top one, and 33 square units on the bottom (the
one with the white square in it). This is because the hypotenuses
of both triangles are not straight lines; both are arcs, with a net
area of one square unit.


So i was right then ?

ohCurry's paradox

The explanation means you were half right.

Congrates to the winner

the answer is:
The extra square results from the assumption that the hypotenuses of the two smaller triangles are in an exact straight line. The discrepancy amounts to about three percent of the large triangle's area.